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Pré-Publication, Document De Travail Année : 2024

Growth condition on the generator of BSDE with singular terminal value ensuring continuity up to terminal time

Dorian Cacitti-Holland
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Laurent Denis
Alexandre Popier

Résumé

We study the limit behavior of the solution of a backward stochastic differential equation when the terminal condition is singular, that is it can be equal to infinity with a positive probability. In the Markovian setting, Malliavin's calculus enables us to prove continuity if a balance condition between the growth w.r.t. y and the growth w.r.t. z of the generator is satisfied. As far as we know, this condition is new. We apply our result to liquidity problem in finance and to the solution of some semi-linear partial differential equation ; the imposed assumption is also new in the literature on PDE.
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Dates et versions

hal-04449583 , version 1 (09-02-2024)

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  • HAL Id : hal-04449583 , version 1

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Dorian Cacitti-Holland, Laurent Denis, Alexandre Popier. Growth condition on the generator of BSDE with singular terminal value ensuring continuity up to terminal time. 2024. ⟨hal-04449583⟩
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